May 12th, 2019 at 8:05:19 AM
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Confusion on ANYONE'S part is just like drunkenness, eventually one sobers up and the windfall dries up. So I would not bank on any erroneous payout continuing.Quote:GBAMIf you mean confusion on my part I am certain I have the rules and payouts correct. We play this game a lot

May 12th, 2019 at 8:06:15 AM
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That’s fair haha.

May 12th, 2019 at 10:15:28 AM
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It makes quite a difference being 200/1 rather than 500/1.Quote:GBAMThank you for doing this. The highest payout for 7/7 is 200:1, not 500....

2 8 50 200 = 4.490 629%

2 9 50 200 = 1.639 277%

May 12th, 2019 at 11:25:00 AM
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Quote:charliepatrickIt makes quite a difference being 200/1 rather than 500/1.

2 8 50 200 = 4.490 629%

2 9 50 200 = 1.639 277%

Excellent. I wasn’t sure if the 500 was a typo or if you misread. Thanks so much for doing that. Not terrible either way, but wish it was 9 : 1. It’s a fun bet to hit. Wonder what the base game is

Is it P(4flush)*2 +P(5flush)*8+P(6flush)*50*P(7flush)*200 minus P(3 or 2 or 1 flush)*1

That is odds of winning* amount - odds of losing* wager

Sorry for the bad formatting

I’d love to be able to answer these questions myself

May 12th, 2019 at 1:06:00 PM
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Quote:GBAMExcellent. I wasn’t sure if the 500 was a typo or if you misread. Thanks so much for doing that. Not terrible either way, but wish it was 9 : 1. It’s a fun bet to hit. Wonder what the base game is

Is it P(4flush)*2 +P(5flush)*8+P(6flush)*50*P(7flush)*200 minus P(3 or 2 or 1 flush)*1

That is odds of winning* amount - odds of losing* wager

Sorry for the bad formatting

I’d love to be able to answer these questions myself

Okay, so the first thing that you want to do is figure out the probabilities of a flush. What we are going to start with is the fact that there are:

nCr (52,7) = 133784560

There are 133,784,560 ways to arrange seven cards out of fifty-two. (You will see we multiply by four for the matches, that's because there are four suits, but the way we are doing the combinatorial part we're acting like there is only one suit and making up for it later.)

Seven Card Match:

nCr (13,7) * nCr (39,0) = 1716 * 4 = 6864/133784560 = 0.0000513063689861

Six Card Flush:

nCr (13,6) * nCr (39,1) = 66924 * 4 = 267696/133784560 = 0.002000948390457

Five Card Flush:

nCr (13,5) * nCr (39,2) = 953667*4 = 3814668/133784560 = 0.02851351456

Four Card Flush:

nCr (13,4) * nCr (39,3) = 6534385*4 = 26137540/133784560 = 0.19537037756

You may care about two and three card flushes, but I don't, because they lose just as equally. Thus, I just want to know the overall probability of losing:

1-(0.0000513063689861+0.002000948390457+0.02851351456+0.19537037756) = 0.77406385312

Cool, now we just slap in your paytable:

((0.0000513063689861 * 200) + (0.002000948390457*50) + (0.02851351456* 8) + (0.19537037756*2)) - (.77406385312) = -0.04490628819

That means a house edge of 4.490628819%.

Now, if we change that eight to one to a nine to one:

((0.0000513063689861 * 200) + (0.002000948390457*50) + (0.02851351456* 9) + (0.19537037756*2)) - (.77406385312) = -0.01639277363

We're going to trim that House Edge to 1.639277363%

I like this online calculator for combinatorics (the nCr function):

https://web2.0calc.com/

However, you could just steal the probabilities from Wizard's High Card Flush page:

https://wizardofodds.com/games/high-card-flush/

Found under the, "Flush Bet," section, which is the same bet you're talking about with a different paytable. I used that to verify what I was doing, naturally.

So, now you know how to do it yourself cleanly and now you know how to cheat to do it!

Vultures can't be choosers.